Open Access
2010 Partially ordered secretaries
Ragnar Freij, Johan Wästlund
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Electron. Commun. Probab. 15: 504-507 (2010). DOI: 10.1214/ECP.v15-1579


The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's task is to choose online a maximal element. This generalizes the classical linear order secretary problem, for which it is known that the selector can succeed with probability $1/e$ and that this is best possible. We describe a strategy for the general problem that achieves success probability at least $1/e$ for an arbitrary partial order.


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Ragnar Freij. Johan Wästlund. "Partially ordered secretaries." Electron. Commun. Probab. 15 504 - 507, 2010.


Accepted: 26 October 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1225.60019
MathSciNet: MR2733374
Digital Object Identifier: 10.1214/ECP.v15-1579

Primary: 60C05
Secondary: 06A07 , 68W20 , 68W27 , 90B50

Keywords: best choice problem , partial order , secretary problem

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